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PhoenixFire
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\[F(x)=\int _{ 1 }^{ ln(x^{ 2 }+e) }{ sin(e^{ t }) } dt\]
Find F'(x).
Not sure how to do this, I understand from the Fundamental Theorem of Calculus that
\[F'(x)=\frac { d }{ dx } \int _{ a }^{ x }{ f(t) } dt=f(x)\]
But what happens to the limit of \(ln(x^2+e)\)?
 11 months ago
 11 months ago
PhoenixFire Group Title
\[F(x)=\int _{ 1 }^{ ln(x^{ 2 }+e) }{ sin(e^{ t }) } dt\] Find F'(x). Not sure how to do this, I understand from the Fundamental Theorem of Calculus that \[F'(x)=\frac { d }{ dx } \int _{ a }^{ x }{ f(t) } dt=f(x)\] But what happens to the limit of \(ln(x^2+e)\)?
 11 months ago
 11 months ago

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bahrom7893 Group TitleBest ResponseYou've already chosen the best response.1
Don't you just do this: Sin(e^b)*(Sin(e^b)) ' where b is the upper limit.
 11 months ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.1
Well, you'd then subtract Sin(e^1) * (Sin(e^1))', but since the derivative of a constant is 0, this term becomes 0, and you're left with just the first one.
 11 months ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.1
Oh and by the way, e^(ln(x)) = x
 11 months ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
I don't understand why you're multiplying f(x) by f'(x) Or do you do the integration, and then derive it? \[\frac{d}{dx}(sin(e^{ln(x^2+e)})sin(e^1))=\frac{d}{dx}sin(x^2+e)=2xcos(x^2+e)=F'(x)\]
 11 months ago
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